We study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically connected with higher bands, closing the gap between the first and second conduction (valence) bands at a certain magnetic flux per unit cell. We also develop a momentum space method for calculating the TBG Hofstadter butterfly, from which we identify three phases where the Hofstadter butterflies of the lowest two bands and the higher bands are connected in different ways. We show this leads to a crossing between the $\nu =4$ Landau fan from the charge neutral point and the zero-field band gap at one flux per moiré unit cell, which corresponds to a magnetic field $25{\theta }^2\mathrm{T}$ (twist angle $\theta$ in degrees). This provides an experimentally testable feature of the fragile topology. In general, we expect it to be a generic feature that the Hofstadter butterfly of the topological bands are connected with the Hofstadter spectra of other bands. We further show the TBG band theory with Zeeman splitting being the most sizable splitting could result in Landau fans at the charge neutral point and half fillings near the magic angle, and we predict their variations under an in-plane magnetic field.

Josephson junctions containing three ferromagnetic layers with noncollinear magnetizations between adjacent layers carry spin-triplet supercurrent under certain conditions. The signature of the spin-triplet supercurrent is a relatively slow decay of the maximum supercurrent as a function of the thickness of the middle ferromagnetic layer. In this work we focus on junctions where the middle magnetic layer is a ${\text{[Co/Pd]}}_N$ multilayer with perpendicular magnetic anisotropy (PMA), while the outer two layers have in-plane anisotropy. We compare junctions where the middle PMA layer is or is not configured as a synthetic antiferromagnet (PMA-SAF). We find that the supercurrent decays much more rapidly with increasing the number $N$ of [Co/Pd] bilayers in the PMA-SAF junctions compared to the PMA junctions. Similar behavior is observed in junctions containing ${\text{[Co/Ni]}}_N$ PMA multilayers. We model that behavior by assuming that each Co/Pd or Co/Ni interface acts as a partial spin filter, so that the spin-triplet supercurrent in the PMA junctions becomes more strongly spin-polarized as $N$ increases, while the supercurrent in the PMA-SAF junctions is suppressed with increasing $N$. We also address a question raised in a previous work regarding how much spin-singlet supercurrent is transmitted through our nominally spin-triplet junctions. We do that by comparing spin-triplet junctions with similar junctions where the order of the magnetic layers has been shuffled. The results of this work are expected to be helpful in designing spin-triplet Josephson junctions for use in cryogenic memory.

We introduce a deep neural network to model in a symmetry preserving way the environmental dependence of the centers of the electronic charge. The model learns from ab initio density functional theory, wherein the electronic centers are uniquely assigned by the maximally localized Wannier functions. When combined with the deep potential model of the atomic potential energy surface, the scheme predicts the dielectric response of insulators for trajectories inaccessible to direct ab initio simulation. The scheme is nonperturbative and can capture the response of a mutating chemical environment. We demonstrate the approach by calculating the infrared spectra of liquid water at standard conditions, and of ice under extreme pressure, when it transforms from a molecular to an ionic crystal.

We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not equilibrate. It constitutes an example of persistent nonstationarity in a quantum many-body system that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries. We discuss how the ensuing persistent oscillations that seemingly violate one of the most fundamental laws of physics could be observed experimentally.

Confinement of excitations induces quasilocalized dynamics in disorder-free isolated quantum many-body systems in one spatial dimension. This occurrence is signaled by severe suppression of quantum correlation spreading and of entanglement growth, long-time persistence of spatial inhomogeneities, and long-lived coherent oscillations of local observables. In this work, we present a unified understanding of these dramatic effects. The slow dynamical behavior is shown to be related to the Schwinger effect in quantum electrodynamics. We demonstrate that it is quantitatively captured for long-time scales by effective Hamiltonians exhibiting Stark localization of excitations and weak growth of the entanglement entropy for arbitrary coupling strength. This analysis explains the phenomenology of real-time string dynamics investigated in a number of lattice gauge theories, as well as the anomalous dynamics observed in quantum Ising chains after quenches. Our findings establish confinement as a robust mechanism for hindering the approach to equilibrium in translationally invariant quantum statistical systems with local interactions.

We report the discovery of ${\mathrm{Zr}}_3\mathrm{Ir}$ as a structurally different type of unconventional noncentrosymmetric superconductor (with $T_c=2.3$ K), here investigated mostly via muon-spin rotation/relaxation ($\mu \mathrm{SR}$) techniques. Its superconductivity was characterized using magnetic susceptibility, electrical resistivity, and heat capacity measurements. The low-temperature superfluid density, determined via transverse-field $\mu \mathrm{SR}$ and electronic specific heat, suggests a fully gapped superconducting state. The spontaneous magnetic fields, revealed by zero-field $\mu \mathrm{SR}$ below $T_c$, indicate the breaking of time-reversal symmetry in ${\mathrm{Zr}}_3\mathrm{Ir}$ and hence the unconventional nature of its superconductivity. By using symmetry arguments and electronic-structure calculations we obtain a superconducting order parameter that is fully compatible with the experimental observations. Hence, our results clearly suggest that ${\mathrm{Zr}}_3\mathrm{Ir}$ represents a structurally different member of noncentrosymmetric superconductors with broken time-reversal symmetry.

${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ is an insulating skyrmion-host material with a magnetoelectric coupling giving rise to an electric polarization with a characteristic dependence on the magnetic-field $\vec{H}$. We report a magnetic force microscopy imaging of the helical real-space spin structure on the surface of a bulk single crystal of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. In the presence of a magnetic field, the helimagnetic order, in general, reorients and acquires a homogeneous component of the magnetization, resulting in a conical arrangement at larger fields. We investigate this reorientation process at a temperature of 10 K for fields close to the crystallographic $\langle 110\rangle$ direction that involves a phase transition at $H_{c1}$. Experimental evidence is presented for the formation of magnetic domains in real space as well as for the microscopic origin of relaxation events that accompany the reorientation process. In addition, the electric polarization is measured by means of Kelvin-probe force microscopy. We show that the characteristic field dependency of the electric polarization originates in this helimagnetic reorientation process. Our experimental results are well described by an effective Landau theory previously invoked for MnSi, that captures the competition between magnetocrystalline anisotropies and Zeeman energy.

The energy vs crystal momentum $E$($k$) diagram for a solid (band structure) constitutes the road map for navigating its optical, magnetic, and transport properties. By selecting crystals with specific atom types, composition, and symmetries, one could design a target band structure and thus desired properties. A particularly attractive outcome would be to design energy bands that are split into spin components with a momentum-dependent splitting, as envisioned by Pekar and Rashba [Zh. Eksp. Teor. Fiz. 47, 1927 (1964)], enabling spintronic application. The current paper provides “design principles” for wave-vector dependent spin splitting (SS) of energy bands that parallel the traditional Dresselhaus and Rashba spin-orbit coupling (SOC)–induced splitting, but originates from a fundamentally different source—antiferromagnetism. We identify a few generic antiferromagnetic (AFM) prototypes with distinct SS patterns using magnetic symmetry design principles. These tools allow also the identification of specific AFM compounds with SS belonging to different prototypes. A specific compound—centrosymmetric tetragonal $\mathrm{Mn}{\mathrm{F}}_2$—is used via density functional band-structure calculations to quantitatively illustrate one type of AFM SS. Unlike the traditional SOC-induced effects restricted to noncentrosymmetric crystals, we show that antiferromagnetic-induced spin splitting broadens the playing field to include even centrosymmetric compounds, and gives SS comparable in magnitude to the best known (“giant’” SOC effects, even without traditional SOC, and consequently does not rely on the often-unstable high atomic number elements required for high SOC. We envision that use of the current design principles to identify an optimal antiferromagnet with spin-split energy bands would be beneficial for efficient spin-charge conversion and spin-orbit torque applications without the burden of requiring compounds containing heavy elements.

We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system we calculate the energy spectrum and quantized Hall conductivities at each spectral gap by using a continuum Hamiltonian that satisfies the magnetotranslation condition. We show that the Hofstadter butterfly spectra of AB-AB and AB-BA stackings differ significantly, even though their zero magnetic field band structures closely resemble; the spectrum of AB-AB has valley degeneracy, which can be lifted by applying interlayer potential asymmetry, while the spectrum of AB-BA has no such degeneracy in any case. We explain the origin of the difference from the perspectives of lattice symmetry and band topology.

Unconventional quasiparticle excitations in condensed matter systems have become one of the most important research frontiers. Beyond twofold and fourfold degenerate Weyl and Dirac fermions, threefold, sixfold, and eightfold symmetry protected degeneracies have been predicted. However they remain challenging to realize in solid state materials. Here the charge density wave compound $\mathrm{TaT}{\mathrm{e}}_4$ is proposed to hold eightfold fermionic excitation and Dirac point in energy bands. High quality $\mathrm{TaT}{\mathrm{e}}_4$ single crystals are prepared, where the charge density wave is revealed by directly imaging the atomic structure and a pseudogap of about 45 meV on the surface. Shubnikov-de Haas oscillations of $\mathrm{TaT}{\mathrm{e}}_4$ are consistent with band structure calculation. Scanning tunneling microscopy/spectroscopy reveals atomic step edge states on the surface of $\mathrm{TaT}{\mathrm{e}}_4$. This work uncovers that the charge density wave is able to induce new topological phases and sheds new light on the novel excitations in condensed matter materials.

Structural phase transitions described by Mexican hat potentials should in principle exhibit aspects of Higgs and Goldstone physics. Here, we investigate the relationship between the phonons that soften at such structural phase transitions and the Higgs- and Goldstone-boson analogs associated with the crystallographic Mexican hat potential. We show that, with the exception of systems containing only one atom type, the usual Higgs and Goldstone modes are represented by a combination of several phonon modes, with the lowest-energy phonons of the relevant symmetry having substantial contribution. Taking the hexagonal manganites as a model system, we identify these modes using Landau theory, and predict the temperature dependence of their frequencies using parameters obtained from density functional theory. Separately, we calculate the additional temperature dependence of all phonon mode frequencies arising from thermal expansion within the quasiharmonic approximation. We predict that Higgs-mode softening will dominate the low-frequency vibrational spectrum of ${\mathrm{InMnO}}_3$ between zero Kelvin and room temperature, whereas the behavior of ${\mathrm{ErMnO}}_3$ will be dominated by lattice expansion effects. We present temperature-dependent Raman scattering data that support our predictions, in particular confirming the existence of the Higgs mode in ${\mathrm{InMnO}}_3$.

The one-dimensional (1D) Affleck-Kennedy-Lieb-Tasaki (AKLT) model is a paradigm of antiferromagnetism, and its ground state exhibits symmetry-protected topological order. On a two-dimensional (2D) lattice, the AKLT model has recently gained attention because it too displays symmetry-protected topological order, and its ground state can act as a resource state for measurement-based quantum computation. While the 1D model has been shown to be gapped, it remains an open problem to prove the existence of a spectral gap on the 2D square lattice, which would guarantee the robustness of the resource state. Recently, it has been shown that one can deduce this spectral gap by analyzing the model's boundary theory via a tensor network representation of the ground state. In this work, we express the boundary state of the 2D AKLT model in terms of a classical loop model, where loops, vertices, and crossings are each given a weight. We use numerical techniques to sample configurations of loops and subsequently evaluate the boundary state and boundary Hamiltonian on a square lattice. As a result, we evidence a spectral gap in the square-lattice AKLT model. In addition, by varying the weights of the loops, vertices, and crossings, we indicate the presence of three distinct phases exhibited by the classical loop model.

Spin transfer across the interface of magnetic insulator/heavy metal is dominated by the magnetic state at interface. Utilizing aberration corrected scanning transmission electron microscopy and electron energy loss spectroscopy, we demonstrate the existence of metallic $\mathrm{F}{\mathrm{e}}^0$ atoms at YIG/Pt interface. The observed spin pumping signal is linearly proportional to total $\mathrm{F}{\mathrm{e}}^0$ magnetic moments at YIG/Pt interface, revealing the critical role of the interfacial magnetic moments on spin transfer. In addition, PtFe alloying might contribute to a channel of spin sink at YIG/Pt interface.

Motivated by recent reports of superconductivity in Sr-doped ${\mathrm{NdNiO}}_2$ films on ${\mathrm{SrTiO}}_3$(001) [Nature (London) 572, 624 (2019)], we explore the role of the polar interface on the structural and electronic properties of ${\mathrm{NdNiO}}_n/{\mathrm{SrTiO}}_3$(001) ($n=2,3$) by performing first-principles calculations including a Coulomb repulsion term. For infinite-layer nickelate films ($n=2$), electronic reconstruction drives the surprising emergence of a two-dimensional electron gas (2DEG) at the interface involving a strong occupation of the Ti $3d$ states. This effect is more pronounced than in ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$(001) and accompanied by a substantial reconstruction of the Fermi surface: a depletion of the self-doping Nd $5d$ states and an enhanced Ni $e_g$ orbital polarization reaching up to $35\%$ at the surface, reflecting a single hole in the $3d_{x^2-y^2}$ states, i.e., cupratelike behavior. In contrast, no 2DEG forms for perovskite films ($n=3$) or if a single perovskite layer persists at the interface. We show that the topotactic reaction from the perovskite to the infinite-layer phase is confined to the nickelate film, whereas the ${\mathrm{SrTiO}}_3$ substrate remains intact.

The angular momentum compensation temperature $T_{\mathrm{A}}$ of ferrimagnets has attracted much attention because of high-speed magnetic dynamics near $T_{\mathrm{A}}$. We show that NMR can be used to investigate domain-wall dynamics near $T_{\mathrm{A}}$ in ferrimagnets. We performed ${}^{57}\mathrm{Fe}\text{−}\mathrm{NMR}$ measurements on the ferrimagnet ${\mathrm{Ho}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ with $T_{\mathrm{A}}=245$ K. In a multidomain state, the NMR signal is enhanced by domain-wall motion. We found that the NMR signal enhancement shows a maximum at $T_{\mathrm{A}}$ in the multidomain state. The NMR signal enhancement occurs due to increasing domain-wall mobility toward $T_{\mathrm{A}}$. We develop the NMR signal enhancement model involves domain-wall mobility. Our study shows that NMR in multidomain state is a powerful tool to determine $T_{\mathrm{A}}$, even from a powder sample and it expands the possibility of searching for angular momentum-compensated materials.

Exotic quantum phases including topological states and non-Fermi liquids may be realized by quantum states with total angular momentum $j=\frac{3}{2}$, as manifested in HgTe and pyrochlore iridates. Recently, an exotic superconducting state with a nonzero density of states of zero-energy Bogoliubov (BG) quasiparticles, the Bogoliubov Fermi surface (BG-FS), was also proposed in a centrosymmetric $j=\frac{3}{2}$ system, protected by a $Z_2$ topological invariant. Here, we consider interaction effects of a centrosymmetric BG-FS and demonstrate its instability by using mean-field and renormalization group analysis. The Bardeen-Cooper-Schrieffer (BCS)-type logarithmical enhancement is shown in fluctuation channels associated with inversion symmetry. Thus, we claim that the inversion-symmetry instability is an intrinsic characteristic of a BG-FS under generic attractive interactions between BG quasiparticles. In drastic contrast to the standard BCS superconductivity, a Fermi surface may generically survive even with the instability. We propose the experimental setup, a second-harmonic-generation experiment with a strain gradient, to detect the instability. Possible applications to iron-based superconductors and heavy-fermion systems, including FeSe, are also discussed.

It was recently pointed out that Fermi surfaces can remain even in superconductors under symmetric spin-orbit interaction and broken time-reversal symmetry. Using the linear response theory, we study the instability of such systems toward ordering, which is an intrinsic property of Fermi surfaces. The ordered states are classified into diagonal and off-diagonal ones, which respectively indicate the Pomeranchuk instability and Cooper pairing not of original electron but of Bogoliubov particles (bogolons). The corresponding order parameters are expanded by multipole moments (diagonal order parameter) and multiplet pair amplitudes (off-diagonal order parameter) of original electrons, which are induced by the internal fields arising from bogolon ordering. While the bogolons' order parameters partially inherit the characters of the original electrons, many order parameter components mix with similar magnitude. Hence, there is no clear-cut distinction for whether the phase transition is diagonal or off-diagonal ordering in terms of the original electrons. These ordering instabilities inside the superconducting states provide insights into superconductors which have the second phase transition below the first transition temperature.

The synthesis, crystal structure, and physical properties (magnetization, resistivity, heat capacity) in combination with theoretical calculations of the electronic structure and phonon properties are reported for intermetallic compounds $\mathrm{Li}{\mathrm{Pd}}_{2}X$ ($X=\mathrm{Si}$, Ge, and Sn). LeBail refinement of powder x-ray diffraction data confirms that all compounds belong to the Heusler family (space group $Fm\text{−}3m$, No. 225). The lattice parameter increases with atomic size of X, and its value varies from $a=5.9059\left(4\right)\AA$ for $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Si}$ and $a=6.0082\left(3\right)\AA$ for $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Ge}$, to $a=6.2644\left(1\right)\AA$ for $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Sn}$. The first compound, $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Si}$, has apparently not been previously reported. All measured quantities demonstrate that $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Ge}$ exhibits superconductivity below $T_c=1.96\mathrm{K}$ and the normal- and superconducting-state data indicate that it is a weak-strength type-I superconductor ($C/\gamma T_c=1.38$) with electron-phonon coupling constant ${\lambda }_{e-p}=\left(0.53-0.56\right)$. $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Si}$ and $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Sn}$ are not superconducting above 1.68 K. The experimental observations are supported by theoretical calculations which show that $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Ge}$ has the highest computed ${\lambda }_{e-p}$ and $T_c$ of the group. A strong softening of the acoustic phonon mode is calculated, and in the case of $X=\mathrm{Ge}$ and Sn, imaginary phonon frequencies were computed. The soft mode is most pronounced in the case of $\mathrm{Li}{\mathrm{Pd}}_2\mathrm{Ge}$, which suggests its correlation with superconductivity.

We report on the observation of edge electric currents excited in bilayer graphene by terahertz laser radiation. We show that the current generation belongs to the class of second order in electric field phenomena and is controlled by the orientation of the THz electric field polarization plane. Additionally, applying a small magnetic field normal to the graphene plane leads to a phase shift in the polarization dependence. With increasing the magnetic field strength, the current starts to exhibit $1/B$-magneto-oscillations with a period consistent with that of the Shubnikov–de Haas effect and amplitude by an order of magnitude larger as compared to the current at zero magnetic field measured under the same conditions. The microscopic theory developed shows that the current is formed in the edge's vicinity limited by the mean-free path of carriers and the screening length of the high-frequency electric field. The current originates from the alignment of the free carrier momenta and dynamic accumulation of charge at the edges, where the $P$-symmetry is naturally broken. The observed magneto-oscillations of the photocurrent are attributed to the formation of Landau levels.

We solve the anisotropic, full-bandwidth, and nonadiabatic Eliashberg equations for phonon-mediated superconductivity by fully including the first vertex correction in the electronic self-energy. The nonadiabatic equations are solved numerically here without further approximations, for a one-band model system. We compare the results to those that we obtain by adiabatic full-bandwidth, as well as Fermi-surface-restricted Eliashberg-theory calculations. We find that nonadiabatic contributions to the superconducting gap can be positive, negative, or negligible, depending on the dimensionality of the considered system, the degree of nonadiabaticity, and the coupling strength. We further examine nonadiabatic effects on the transition temperature and the electron-phonon coupling constant. Our treatment emphasizes the importance of overcoming previously employed approximations in estimating the impact of vertex corrections on superconductivity and opens a pathway to systematically study vertex correction effects in systems such as high-$T_c$, flat band, and low-carrier density superconductors.